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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.07033 |
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Table of Contents:
- A map is \emph{vertex-reversing} if it admits an arc-transitive automorphism group with dihedral vertex stabilizers. This paper classifies solvable vertex-reversing maps whose edge number and Euler characteristic are coprime. The classification establishes that such maps comprise three families: $\D_{2n}$-maps, $(\ZZ_{m}{:}\D_{4})$-maps, and $(\ZZ_{m}.§_4)$-maps, where $m$ is odd. Our classification is based on an explicit characterization obtained of finite almost Sylow-cyclic groups, associated with a shorter proof and explicit description of generators and relations.